The book contains more than 600 problems and theorems on geometric inequalities, mainly for convex polygons and polyhedra. Among the tasks there are both easy and difficult; At various times, some of the problems were offered at mathematical Olympiads for schoolchildren. Some problems are given instructions, and sometimes complete solutions. The book is intended for students, but may be of interest to teachers, students and anyone interested in mathematics. The problems contained in it can be used in the work of mathematical circles. By solving them, students will get acquainted with the proofs of interesting geometric theorems, very different from what they know in the school course, and will even be able to try to solve problems that have not yet been solved by anyone.